J. Resour. Ecol. 2010 1(2) 123-134DOI:10.3969/j.issn.1674-764x.2010.02.004www.jorae.cn

Vol.1, No.2

Received: 2010-02-06 Accepted: 2010-04-30The author: XU Ming. Email: Ming.Xu@gatech.edu.

1 IntroductionThe fields of ecology and economics have been borrow-ing ideas from each other for a long time. Concepts ineconomics, such as producers and consumers, have beenapplied in ecological research from early twentieth centu-ry (Worster 1994). Principles of ecology have also beenused to study the environmental issues for industrial andeconomic systems (Graedel et al. 1995; Ayres et al. 1996;Allenby 1999; Suh 2004b). Recently, it is generallyagreed that the study of sustainability should pay specialattention to the integrated ecological-economic systemswhich emphasize both physical aspects of the system,such as material or energy flows, and non-physical as-pects, such as monetary or information flows.Input-output analysis (IOA) is widely regarded as a

powerful approach to illustrate the correlations among en-

tities in ecological-economic systems, especially for na-tional economies. Although there are various types ofIOA applications on studying ecological-economic sys-tems, the principles and theories are basically same andwere first developed by Leontief (1936; 1941). Generally,there are two main areas in which IOA is applied to studyecological-economic systems. One is well-known as phys-ical input-output tables (PIOTs) which present the inputand output material flows in physical units for all sectorsof an economic system (Kneese et al. 1970). The other ap-plication is mainly based on monetary input-output tables(MIOTs), which are used to present economic connec-tions between economic sectors, with extensional informa-tion about physical interactions between the ecologicalsystem and the economic system (Suh 2005). In general,MIOT-related research has been applied more widely be-cause its data availability is much better than PIOT-relat-

XU Ming

Brook Byers Institute for Sustainable Systems, Georgia Institute of Technology, Atlanta, GA 30332-0595, U.S.A.

Abstract:

Key words:

Journal of Resources and Ecology Vol.1 No.2, 2010

ed research.In this article, we first briefly summarize the previous

research on ecological-economic systems using IOAmeth-ods. A model called physical input monetary output(PIMO) is then developed to integrate economic informa-tion in monetary units and societal metabolism informa-tion in physical units. A case study of PIMO applicationon China s economy is provided in the following section.Finally, discussions and future studies are concluded.

2 Input-output analysis onecological-economic systems

The IOA model was first developed by Leontief in lastcentury, and has been playing an important role in eco-nomic policy analysis. The basic input-output frameworkhas two models, quantity model and price model. Thequantity model can use either quantity units, such astonnes steel or units of computers, or monetary units(Duchin 2004). The most widely used input-output modelis in monetary units because of the feasibility of data col-lection and estimation, applicability to national economicaccounting, and capability to balance by simple calcula-tion. At present, MIOTs are available for a large numberof countries as a part of their national account systems(Hubacek et al. 2003). The concept and computationalstructure of IOA, and the format of MIOTs can be re-ferred to various well-known publications, such as Leonti-ef (1966), Miller and Blair (1985), or United Nations(2003).One of the main applications of IOA on ecological-eco-

nomic systems is the compilation of PIOTs. The founda-tion of PIOT research was first made by Kneese et al.(1970). Examples of PIOTs published can be found inKratterl and Kratena (1990); Kratena et al. (1992); Konijnet al. (1997); Stahmer et al. (1997); Pedersen (1999); Neb-bia (2000); Stahmer (2000); M enp (2002); and Hoeks-tra (2003). Based on the principles of IOA, PIOTs assem-ble physical data to present the materials exchangingamong economic sectors. However, because of the rela-tively young history of physical input-output accounting,no standard method for the PIOT compilation has been de-veloped yet. Therefore, existing PIOTs differ from eachother in conventions and definitions more or less (e.g.,Hubacek et al. 2003; Suh 2004a; Giljum et al. 2004;Weisz et al. 2006). The lack of standard compiling meth-od is one of the main bottlenecks for PIOT application to-gether with the difficulty of data collection.The other main application of IOA to study ecologi-

cal-economic systems extends MIOTs with mixed-unit da-ta. In 1970, Leontief already introduced an input-output

model to study the relationship between environmentalpollution and economic structures by adding a row of pol-lutants and a column of anti-pollution in the conventionalinput-output table (Leontief 1970). Energy issues werewidely discussed using IOA in 1970s (Hannon 1973; Bull-ard et al. 1975; Herendeen 1978). However, the method ofIOA did not begin to attract broader attentions until in1990s. To study the specific environmental impact of eco-nomic activities, Moriguchi et al. (1993) used input-out-put data to assess the life cycle carbon dioxide (CO2) im-pacts of cars in Japan; Suh (2006) used IOA to study theimpacts of economic activities on climate change fromthe perspective of structure characteristics; Hawkins et al.(2007) developed a mixed-unit model combining themethods of life cycle assessment (LCA) and material flowanalysis (MFA) to track material flows and economictransactions throughout the economy; and the environ-mental input-output life cycle assessment (EIO-LCA)model developed at Carnegie Mellon University can quan-titatively evaluate the environmental impacts of a productor service over the course of its entire life-cycle (Hen-drickson et al. 2006). MIOTs are also modified with ex-tended sectors to study the particular environmental is-sues, such as land use accounting (Hubacek et al. 2001),waste management (Nakamura et al. 2002; 2006), or envi-ronmental burdens caused by international trades (Peterset al. 2006a; 2006b; 2008; Weber et al. 2007). All thesestudies focused on particular environmental impacts or en-vironmental impacts caused by particular economic activi-ties. In this article, our approach differs from these studiessince the entire ecological-economic system is quantita-tively simulated in the PIMO model, but do not only con-sider specific environmental issues.In the next section, the PIMO model is introduced,

which is easy to implement using a relatively standardcompilation framework. It also provides new tools for eco-logical economics, industrial ecology, and related fields.

3 Physical input monetary output modelThe PIMO model focuses on an economic system whichcan be divided into various sectors. The surrounding eco-logical system has material exchanges with the economicsystem. In this section, the PIMO model is introduced inaspects of conceptual model, PIMO table, PIMO analysis,and uncertainty.

3.1 Conceptual modelA conceptual societal metabolism model of an ecologi-cal-economic system is illustrated as Figure 1. In the con-ceptual model, the economic system contains two sectors

XU Ming: Development of the Physical Input Monetary Output Model for Understanding Material Flows within Ecological-Economic Systems

each of which extracts two types of resources from theecological system and emits two types of wastes to theecological system. It should be specially stated that theterm of resource means raw materials, such as mineralores or crude oil, extracted directly from the ecologicalsystem by the economic system. On the other hand, theterm of waste refers to the wastes and emissions gener-ated by the economic sectors and returning to the ecologi-cal system without any further treatment. There is no eco-nomic cost for those materials in the conventional eco-nomic analysis including IOA.The economic system can be modeled by IOA. There-

fore, it is possible and reasonable to quantitatively repre-sent the correlations between economic sectors by MIOTsand the connections between the ecological system andthe economic system by the method of MFA.To make the PIMO model easy to compile, the above

conceptual model is modified as illustrated in Figure 2. Inthe conceptual PIMO model, wastes emitted by the eco-nomic system are regarded as non-positive (not onlynegative because specific types of wastes could be zero)inputs from the ecological system to the economic sys-tem, while resources are known as positive inputs. As aresult, the conceptual PIMO model contains physicalflows, both positive and non-positive, in the input sideand monetary flows in the output side, which is also thereason why the model is described as physical input andmonetary output model.

3.2 PIMO tableBased on MIOTs, extra rows can be added to extend to

PIMO tables. Table 1 is the basic structure of the PIMO ta-ble. From top to bottom, the PIMO table can be dividedinto three parts. The first part is the conventional MIOT,which represents the structure of the economic system.The following part is the resource table and the last part isthe waste table. The latter two parts represent the connec-tion between the ecological system and the economic sys-tem. The classification of economic sectors and resourceor waste categories in the PIMO table differs from re-search goals and available data. In general, it is easy tocompile a PIMO table based on the MIOT classificationof economic sectors which were already applied widely,especially for national economies, such as the system ofnational accounts (SNA) and the system of environmentaland economic accounts (SEEA) provided by the UnitedNations (1993; 2003).The symbols in the first part of the PIMO table are the

same with those in MIOTs. Other symbols will be intro-duced thereafter together with basic computational frame-work of the PIMO model.Consider that the ecological-economic system has n

economic sectors, m categories of resources, and k catego-ries of wastes. Let rij indicate the physical amount of theresource input from the category i to the sector j, where

rij 0. Therefore, let measure the total amount

of resource input to the economic system from the catego-ry i. Similarly, w(m+i)j indicates the physical amount of neg-ative waste input from the category i to the sector j, whichis actually the waste output from the sector j to the catego-ry i, where w(m+i)j 0. Thus, Wm+i can be used to represent

Fig. 1 The conceptual societal metabolism model of an eco-logical-economic system.

Resource1

Resource2

Waste 1

Waste 2

Sector1

Sector2

Finalproduction

Y1

Finalproduction

Y2

r11

r12

r21

r22

w11

w12

w21

w22

x11

x12 x21

x22

Fig. 2 The conceptual PIMO model.

Resource2

Sector1

Sector2

Finalproduction

Y1

Finalproduction

Y2

Waste 1

Waste 2

Ecological system Economic system Ecological system Economic system

Journal of Resources and Ecology Vol.1 No.2, 2010

the total amount of waste output from the economic sys-

tem to the category i, where . .

The computational framework of PIMO model relieson mass balance of the entire economic system and eacheconomic sector. To make the economic data, in monetaryunits, and the material data, in physical units, comparable,ei, material intensity coefficient, is used to indicate the av-erage weight of products of unit price in the sector i. Forthe sector j, the input contains material input from the eco-

logical system, , and the input from eco-

nomic system, , where xij indicates the monetary in-

put from sector i to sector j. The stocks and output of the

sector j contain the output to other economic sectors,

, and the final demand, ejYj, where Yj is the final

demand of sector j. Therefore, the mass balance for a sin-gle economic sector can be expressed by the following

equation, .

For the entire economic system, the input is materials

from the ecological system, . The stocks and

output are final demands, . Thus, the mass balance

of the entire economic system can be expressed as follow-

ing, .

To mathematically present the computational frame-work of PIMO model, two coefficients are introduced.First, the intensities of resource consumption and wastegeneration in different sectors are indicated by the materi-al efficiency coefficient which means the physical amountof materials in the resource or waste category i required

Intermediate M onetary Output Sector

Final Demand

Total Output

M onetary Input

M onetary Output

1 2 n Y X

1 x11 x12 x1n Y1 X1

2 x21 x22 x2n Y2 X2

Intermediate M onetary

Input Sector

n xn1 xn2 xnn Yn Xn

Value-added V V1 V2 Vn

Total Input X X1 X2 Xn

Physical Input Distribution

Physical Input Sector

1 r11 r12 r1n R1

2 r21 r22 r2n R2

Resource Category

m rm1 rm2 rmn Rm

m+1 w(m+1)1 w(m+1)2 w(m+1)n Wm+1

m+2 w(m+2)1 w(m+2)2 w(m+2)n Wm+2

Waste Category

m+k w(m +k)1 w(m+k)2 w(m+k)n Wm+k

Table 1 The PIMO table.

XU Ming: Development of the Physical Input Monetary Output Model for Understanding Material Flows within Ecological-Economic Systems

to produce per unit economic output of the sector j,

where Xj is the total economic output of sector j. Second,the physical distribution of resources and wastes amongeconomic sectors are presented by the material distribu-tion coefficient

which means the portion of physical materials from the re-source or waste category i to the sector j in the total inputamount of that category of resource or waste to the entireeconomic system.The detailed description of the computational frame-

work of the PIMO model can be referred to the Supple-mentary Information.

3.3 PIMO analysisThe most important contribution of PIMO model is tomake societal metabolism internalized in the modelingfor the ecological-economic system. Resource consump-

tion and waste generation are inherently connected witheconomic activities. Secondly, data required by the PIMOmodel are available and cheap for most important coun-tries, which makes the model practical. Moreover, in thePIMO model, raw materials only go to the correspondingextraction sectors. Therefore, one only needs to know thetotal amounts of raw materials extracted and assign themto the corresponding extraction sectors, and does not needto allocate those amounts into all sectors because the in-formation about sectoral resource consumption are ex-pressed by the input-output correlations between the ex-traction sectors and other sectors.In general, the PIMO model can be used to model the

inherent relationship between material flows and econom-ic flows. One can conduct the analysis by making one ofthe parameters exogenous. The performance of the sys-tem, both ecologically and economically, can be simulat-ed from different aspects by changing one of those param-eters. Particularly, the technical coefficient matrix, A, canindicate technology development of the economic system;the final demand vector, Y, can present the structuralchange; and the material efficiency matrix, P=(pij)(m+k)×n, isthe efficiency indicator of societal metabolism.Figure 3 shows the general algorithm of the PIMO anal-

ysis. First, scenarios are set depending on research ques-tions. Variables and constants are then chosen based onthe scenarios. Then, the economic structure and materialintensity coefficient are indicated, respectively, and mate-rial efficiency matrix and material distribution matrix arecompiled. The model calculates the total resource re-quired and waste generated by the economic-ecologicalsystem represented by corresponding scenarios. The sce-narios are checked along each step by the constraints. Fi-nally, further studies about the ecological-economic sys-tem are conducted based on the scenarios.By using the PIMO model, one can compile a PIMO ta-

ble based on an existing MIOT, and then study specificquestions using selected parameters and mathematic cor-relations. This general analysis will be exampled in thefollowing section by a case study for China s ecologi-cal-economic system.

3.4 UncertaintyThere are four major categories of uncertainty in thePIMO approach. First, economic input-output data areusually available only with a three or four-year time lag atbest for most countries. Moreover, detailed economic in-put-output data are only compiled once in several yearsbecause of the costly procedure to obtain necessary infor-mation for a national economy, especially for large coun-

Fig. 3 The general algorithm of PIMO analysis.

Interpretation of economic structureand material intensity

X = (I-A)-1YE = (I-A')-1P'i

Calculation of material efficiencyand material distribution

PX̂ = T̂D = MD'PX + (A'E)X = EX

P'i + A'E = E

Modeling for material requirement andwaste generation, and economic output

B = (I-A) 1

F = PBPX̂ = T̂D = M

Analysis

Constants Variables

Constraint

Scenarios

Journal of Resources and Ecology Vol.1 No.2, 2010

tries including China. Nonetheless, input-output data arestill the cheapest and the most available source for nation-al economy in terms of economic structure and technolo-gy development. Second, the endemic assumption of a lin-ear relationship between societal metabolism and econom-ic change is very common to all current input-outputmethods. Extra uncertainties are introduced when integrat-ing physical data and monetary data together and convert-ing monetary data into data with physical units based onthis assumption. Without a doubt, the interaction betweenecological and economic systems is far more complexthan this at many different scales. Therefore, an importantchallenge for the future is developing more complete datasets and suitable methodologies, potentially based onsome previous work such as dynamic input-output ap-proach (Leontief et al. 1953), to enable more valid model-ing of that complexity. Third, the assumption of homoge-neous products in each sector is fundamental for in-put-output methods. The limitation due to this assumptioncan be improved by developing more data for subsectorswithout increasing the time lag too much. It is no doubt-ful that the disaggregation of economic sectors and mate-rial categories will significantly bring more uncertaintiesbecause the number of parameters is increased. However,it is also easier to improve the data quality for specificsectors or materials at smaller scales, which will reducethe uncertainties on the other hand. This task is particular-ly hard for the PIMO method because one needs to obtainboth economic data and societal metabolism data. Last

but not least, the uncertainty from the data themselves isalso a major concern when doing uncertainty analysis.Various sources are available for data required in thePIMO method. However, only those whose uncertainty isrelatively small or measurable could be chosen as thesource of data. For a national economic system, as wewill present in the case study section, data from the gov-ernment s statistical departments are relatively reliableand the most common source.

4 Case studyThe PIMO model is designed to comprehensively, quanti-tatively, and systematically interpret the interaction be-tween the ecological system and the economic system,but not isolatedly study specific resource-related or envi-ronmental issues. The sustainability issue in China is com-plicated and contains various aspects from resource scarci-ty to environmental pollutant (Liu et al. 2005; Cyranoski2007). The continuously growing economy in China re-quires more resources and will cause more environmentalproblems. Moreover, those resource-related and environ-mental issues are all connected with each other. One sin-gle attempt on a specific aspect, for example, increasingefficiency in one specific sector in terms of energy con-sumption, can affect other sectors of the whole economywhich will influence that sector reversely. Therefore, acomprehensive model is necessary for studying this com-plex system composing of various elements which areconnected and related with each other in a complicated

Fig. 5 Percentage changes of the total requirement for Fer-rous Metal Minerals and the total generation of Sulfur Dioxide(SO2) associated with 10% increase of final demand in one ofthe sectors.

Percentage Percentage

XU Ming: Development of the Physical Input Monetary Output Model for Understanding Material Flows within Ecological-Economic Systems

pattern. The development of PIMO model meets this re-quirement and is especially suitable to comprehensivelystudy the resource-related and environmental issues inChina and the relation with its economic development.In this section, the PIMO model is used to study China s

ecological-economic system to illustrate the impacts onsocietal metabolism due to economic structure characters.A 2002 China PIMO model is assembled based upon 43economic sectors which were aggregated from a 122-sec-tor MIOT, 10 categories of resources, and 6 categories ofwastes. Especially, the waste category of Carbon in Car-bon Dioxide (C in CO2) is used to balance the combustion

process expressed by the reactionC + O2 CO2.The economic input-output data were provided by the

National Bureau of Statistics of China (NBSC) (2006),which also provided the societal metabolism data togetherwith the Editing Committee of China Environmental Year-book (2003); and Xu and Zhang (2007). Details aboutclassification of economic sectors and materials and themodel results can be referred from the Supplementary In-formation.Based on the 2002 China PIMO table compiled, one

can calculate material intensity coefficients for all sectors,

Material intensity coefficient Sector 0.47 Farming 0.35 Forestry 0.30 Animal Husbandry 0.36 Fishery 1.71 Coal Mining and Dressing 0.70 Petroleum and Natural Gas Extraction 2.33 Ferrous Metals Mining and Dressing 2.10 Nonferrous Metals Mining and Dressing 2.65 Nonmetal and Other Minerals Mining and Dressing 0.45 Food Processing 0.62 Food Manufacturing 0.61 Beverage Manufacturing 0.20 Tobacco Processing 0.66 Textile Industry 0.64 Garment Products 1.24 Timber Processing, Bamboo, Cane, Palm Fiber and Straw Products 0.88 Furniture Manufacturing 1.16 Papermaking and Paper Products 0.97 Printing and Record Medium Reproduction 0.79 Cultural, Education and Sports Goods 1.03 Petroleum Refining and Coking 1.38 Raw Chemical Materials and Chemical Products 0.75 Medical and Pharmaceutical Products 1.16 Chemical Fiber 0.71 Rubber Products 1.04 Plastic Products 1.58 Concrete Manufacturing 1.18 Other Nonmetal Mineral Products 1.48 Smelting and Pressing of Ferrous Metals 1.51 Smelting and Pressing of Nonferrous Metals 1.21 Metal Products 0.98 Ordinary Machinery 0.96 Special Purpose Equipment 0.83 Transport Equipment 0.95 Electric Equipment and Machinery 0.71 Electronic and Telecommunications Equipment 0.84 Instruments, Meters, Cultural and Office Machinery 0.69 Other Machinery 6.34 Production and Supply of Electric Power, Steam and Hot Water 1.53 Production and Supply of Gas 3.70 Production and Supply of Tap Water 1.08 Construction 1.06 Tertiary Industry

Table 2 Material intensity coefficients of the 2002 China PIMO model (tonnes per 2002 China yuan).

Journal of Resources and Ecology Vol.1 No.2, 2010

as showed by Table 2. The sector 39, Production and Sup-ply of Electric Power, Steam and Hot Water, has the high-est material intensity coefficient, 6.34 tonnes per Chinayuan in 2002 price (similarly hereinafter). The sector 13,Tobacco Processing, has the lowest value, 0.20 tonnes peryuan. In general, the raw material extraction sectors andthe sectors providing public utilities have higher materialintensity coefficients than the manufacture sectors, ser-vice sectors, and agriculture sectors. As defined above,the material intensity coefficient measures the averageweight of sectoral products with unit price.To address the utility of the PIMO model compiled for

China s economic system, the impacts of economicgrowth on resource consumption and waste generation arestudied. Taking the sector 43, Tertiary Industry, whichcontains all service sectors as the example, Figure 4shows the percentage change of the total amounts of re-sources required and wastes generated due to a 10% in-crease of final demand in the sector 43. Solid waste is themost sensitive waste category influenced by this econom-ic change due to the 3.89% increase, followed by waste-water with 2.63% growth. In the resource categories, therequirement for Petroleum and Natural Gas increases by3.25% in the same scenario, followed by Fresh Waterwith 2.80% growth. Similar analysis can be conducted tosee impacts on the societal metabolism due to other sec-tors changes.The total amounts of resources required or wastes gen-

erated associated with economic changes in different sec-tors are also studied by the PIMO model. As exampled byFerrous Metal Minerals and Sulfur Dioxide (SO2) in Fig-ure 5, the 10% increase of final demand in one of sectorwill cause different percentage change of amounts of re-sources requirement or wastes generation. As expected,both ferrous metals required and SO2 emitted are changeddramatically by Construction and Tertiary Industry be-cause of huge demands of final consumption. The equip-ment manufacturing sectors and the sector of Ferrous Met-als Mining and Dressing can also cause significant in-crease of ferrous metals requirements by growth of thesectroal final demand. For SO2, the equipment manufac-turing sectors also have important influences on the emis-sion amount. The light industry sectors, such as GarmentProducts, and the agriculture sectors, such as Farming,consist of another main group of driving force for SO2

emission. Similar analysis can also be conducted for otherresources and wastes. Moreover, the results showed inFigure 5 can also be referred as an example of quantita-tively sensitive analysis. For instance, the requirement ofFerrous Metal Minerals and the emission of SO2 are more

sensitive to the sectors of Construction and Tertiary Indus-try than to other sectors.

5 ConclusionIn this article, the application of IOA to study ecologi-cal-economic systems is reviewed. A new tool namedPIMO model is developed based on the technique of IOAand the method of MFA to integrate ecological systemsand economic systems. The PIMO model contains a set ofparameters and mathematical correlations. The interactionbetween the ecological system and the economic systemis regarded as the materials input from the former to thelatter, which are quantified in physical units by MFA or re-lated methods. The connection between economic sectorsis modeled by MIOTs in monetary units. Mass balancesof the entire economic system and each economic sectorare compiled to quantitatively synthesize the complex eco-logical-economic systems. The material intensity coeffi-cient is used to convert societal metabolism data in mone-tary unit to data in physical unit.A case study of the PIMO analysis for China is present-

ed. The 2002 PIMO table for China is compiled based onits 2002 MIOT. Necessary integration for economic sec-tors in MIOT is required to meet the availability of MFAdata in the case of China in 2002. The PIMO table com-piled contains 43 economic sectors, 10 resource catego-ries, and 6 waste categories. Mass balances are built foreach sector by the mathematical framework of the PIMOmodel. Studies for China s ecological-economic systemare conducted based on the PIMO table from the perspec-tive of economic structure change.The same as other IOA-related methods, data availabili-

ty is the most difficult bottleneck to be conquered for com-piling a PIMO table. While the development of IOA-relat-ed methods is attracting more and more attentions recent-ly, much more effects should be put in the improvementfor data availability. The most feasible way to improve da-ta availability is to develop international standard for PI-OTs or other national accounting frameworks focusing onnot only economic systems but also ecological-economicsystems. Moreover, the input-output methods have the lin-ear correlation which simplified the complex ecologi-cal-economic systems. It helps to understand the complexsystem, though too much simplification may also lose alot of information.Future work should, where possible, focus on the analy-

sis for structural characters of final consumption. Due tothe lack of data, the Tertiary Industry, which contains fi-nal consumption sectors, is highly aggregated. The influ-ences of final consumption on societal metabolism will be

XU Ming: Development of the Physical Input Monetary Output Model for Understanding Material Flows within Ecological-Economic Systems

uncovered as more information is available for sub-sec-tors in the Tertiary Industry. Furthermore, significant im-provement may be carried out on methodology develop-ment to study the impacts of products prices on societalmetabolism.

AcknowledgementThis The author thanks the support provided by the EnvironmentalResearch and Education Foundation.

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AppendicesAppendix A: Parameter definitionsn, m, k: the ecological-economic system has n eco-

Journal of Resources and Ecology Vol.1 No.2, 2010

nomic sectors, m categories of resources, and k cate-gories of wastes;xij, aij, bij, A, Xi, Yi, Vi: parameters from IOA and MI-OTs;rij: the physical amount of resource input to sector jfrom resource category i, ry 0;Ri: the total amount of input to the economic system

from resource category i, ;

w(m+ i)j: the physical amount of waste output from sec-tor j to waste category i, w(m+i)j 0;Wm + i: the total amount of output from the economic

system to waste category i, ;

ei: material intensity coefficient, the average weight ofproducts per unit price in the sector i;E: material intensity vector, E=(e1, e2, ,en)T

pij: material efficiency coefficient, the physicalamount of materials from resource or waste categoryi required to produce per unit of economic output ofsector j,

P: material efficiency matrix, P=(pij)(m+k)×n;sij: material distribution coefficient, the portion ofphysical materials input from resource or waste cate-gory i to sector j in the total input amount of that cate-gory of resource or waste to the entire economic sys-tem,

S: material distribution matrix, S=(sij)(m+k)×n;G: (m+k)×1 vector of total amount of materials input,including m types of resource and k types of waste,G=(R1, R2, ,Rm, Wm+1, Wm+2, ,Wm+k)T;

is (m+k)×n matrix of material

consumption;

fij: material cumulative input coefficient, ;T=(tij)n×n=(I-A) 1 is the cumulative input matrix;F: (m+ k) × n matrix of cumulative material require-ments, both positive and negative.

Appendix B: Computational frameworkConsider that the ecological-economic system has n

economic sectors, m categories of resources, and k catego-ries of wastes. Let rij indicate the physical amount of theresource input from the category i to the sector j, where

ry 0. Therefore, let measure the total amount of

resource input to the economic system from the categoryi. Similarly, w(m+ i)j indicates the physical amount of nega-tive waste input from the category i to the sector j, whichis actually the waste output from the sector j to the catego-ry i, where w(m+ i)j 0. Thus, Wm+i can be used to representthe total amount of waste output from the economic sys-

tem to the category i, where .

The intensities of resource consumption and waste gen-

eration in different sectors are indicated by the material ef-ficiency coefficient which means the physical amount ofmaterials in the resource or waste category i required toproduce per unit economic output of the sector j,

where Xj is the total economic output of sector j. P=(pij)(m+k)×n represents the material efficiency matrix.The physical distribution of resources and wastes

among economic sectors are presented by the material dis-tribution coefficient

which means the portion of physical materials from theresource or waste category i to the sector j in the total in-put amount of that category of resource or waste to the en-tire economic system. D=(dij) (m + k) × n indicates the materialdistribution matrix.From the definition of the material efficiency matrix

and the material distribution matrix, the relationship be-tween P and D can be expressed as

(1)

where X=(X1, X2, , Xn)T is n×1 vector of total economicoutputs; T=(R1, R2, ,Rm, Wm+1, Wm+2, ,Wm+k)T is (m+k)×1vector of total materials inputs, including m types of re-

sources and k types of wastes (negative); is

(m+k)×n matrix of material consumption; and hat (^) di-

agonalizes a vector.The mass balance for the entire economic system can

be expressed by

XU Ming: Development of the Physical Input Monetary Output Model for Understanding Material Flows within Ecological-Economic Systems

where ei, ecological-economic coefficient (e-coefficient),indicates the average weight of products of unit price inthe sector i; and Yi is the final demand of sector i. Theleft-hand-side (LHS) of the equation presents net physicalamount of the material inputs to the economic system,while the right-hand-side (RHS) is the physical value ofthe monetary outputs (final demand). Rewrite the massbalance equation into the matrix format,iPX = E'Y (2)where i=(1,1, ,1) is 1×(m+k) unit vector; Y=(Y1, Y2, ,Yn)T is n×1 vector of final demand; and E=(e1, e2, , en)T isn×1 vector of e-coefficients.Consider each sector as a control system, and derive

mass balance for the sector j,

where xij indicates the monetary input from sector i to sec-tor j. The LHS of the equation is the summation of the ma-terial inputs to the sector j from categories of resourcesand wastes (negative), and other economic sectors, andthe RHS is the output summation from the sector j. The

RHS can be rewritten as . Therefore, the

mass balance of sector j can be expressed as

Rewrite the sectoral mass balance equation into the ma-trix format as

(3)where A is n×n technical coefficient matrix.From the definition of material efficiency coefficients,

one can get,rij=xjpij, (i=1,2, ,m);

w(m+i)j=xjp(m+i)j, (i=1,2, ,k)Substitute the above equations into the sectoral mass

balance equation and derive

where represents the technical coefficients.Rewrite the equation above by canceling Xj in both RHSand LHS,

and the matrix format isP'i + A'E = E (4)where i=(1,1, ,1)T is (m+k)×1 unit vector. Equation (3)and equation (4) are both derived from the sectoral massbalance equation. Thus they are equivalent from each oth-er. However, equation (4) is much easier for effectivecomputation because it does not need the material distri-bution matrix D which is required in equation (3). Fromequation (4), one can calculated e-coefficients based onthe technical matrix and the material efficiency matrix,E = (I-A') 1P'i (5)Similar with IOA, there are also cumulative effects in

the PIMO model for the physical inputs. Define fij as thematerial cumulative input coefficient, which means the cu-mulative net material input of category i caused by perunit of output of sector j. fij can be calculated as

where bij is the cumulative input coefficient. Rewritethe above equation to matrix format asF = PB (6)where F=(fij)(m+k)×n is the matrix of cumulative material re-quirements, and B=(bij)n × n=(I-A) 1 is the cumulative inputmatrix.

Appendix C: Sector and material classifications

Table S1 Classification of sectors in China s economic system.

1 Farming2 Forestry3 Animal Husbandry4 Fishery5 Coal Mining and Dressing6 Petroleum and Natural Gas Extraction

No. Sector

7 Ferrous Metals Mining and Dressing8 Nonferrous Metals Mining and Dressing9 Nonmetal and Other Minerals Mining andDressing

10 Food Processing11 Food Manufacturing

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Brook Byers GA 30332-0595

Table S2 Classification of resources and wastes.

Continued table S1

12 Beverage Manufacturing13 Tobacco Processing14 Textile Industry15 Garment Products16 Timber Processing, Bamboo, Cane, Palm Fiber and

Straw Products17 Furniture Manufacturing18 Papermaking and Paper Products19 Printing and Record Medium Reproduction20 Cultural, Education and Sports Goods21 Petroleum Refining and Coking22 Raw Chemical Materials and Chemical Products23 Medical and Pharmaceutical Products24 Chemical Fiber25 Rubber Products26 Plastic Products27 Concrete Manufacturing

28 Other Nonmetal Mineral Products29 Smelting and Pressing of Ferrous Metals30 Smelting and Pressing of Nonferrous Metals31 Metal Products32 Ordinary Machinery33 Special Purpose Equipment34 Transport Equipment35 Electric Equipment and Machinery36 Electronic and Telecommunications Equipment37 Instruments, Meters, Cultural and Office Machinery38 Other Machinery39 Production and Supply of Electric Power, Steam and Hot

Water40 Production and Supply of Gas41 Production and Supply of Tap Water42 Construction43 Tertiary Industry

No. MaterialA Farm CropsB Forest ProductsC Livestock ProductsD Aquatic ProductsE CoalF Petroleum and Natural GasG Ferrous Metal MineralsH Nonferrous Metal MineralsI Nonmetal MineralsJ Fresh WaterK Solid WasteL Carbon in Carbon Dioxide (C in CO2)M Sulfur Dioxide (SO2)N Industrial SootO Industrial DustP Waste Water